CMS-PAS-SMP-23-003

CMS-PAS-SMP-23-003
Search for charged lepton flavor violating Z and Z' boson decays in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
13 March 2025

Abstract: A search for charged lepton flavor violating decays of the Z boson is performed using data from proton-proton collisions at $\sqrt{s}=$ 13 TeV collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The Z $\rightarrow$ e $\mu$ , Z $\rightarrow$ e $\tau$ , and Z $\rightarrow\mu\tau$ decays are considered separately, where hadronic and different-flavor leptonic $\tau$ decays are used in the latter two searches. The data are found to be consistent with expectations from the standard model. For the Z $\rightarrow$ e $\mu$ channel the observed (expected) 95% CL upper limit on the branching fraction is 1.9 $\times 10^{-7}$ ( 2.0 $\times 10^{-7}$ ), which is the most stringent direct limit to date on this process. The corresponding limits for the Z $\rightarrow$ e $\tau$ , and Z $\rightarrow\mu\tau$ channels are 13.8 $\times 10^{-6}$ ( 11.4 $\times 10^{-6}$ ) and 12.0 $\times 10^{-6}$ ( 5.3 $\times 10^{-6}$ ), respectively. Additionally, the e $\mu$ final state is used to search for lepton flavor violating decays of resonances in the mass range from 110 to 500 GeV. No significant excess is observed above the predicted background levels.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Invariant mass of the $\mathrm{e}\mu$ system for data (points with error bars) and simulated background (stacked filled histograms) events passing the baseline selection. The hatched histogram shows a hypothetical $\mathrm{Z}\to\mathrm{e}\mu$ signal normalized to a branching fraction of 1.0 $\times10^{-5}$ . The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 2: The left-band plot shows the unity-normalized distributions of the $\mathrm{Z}\to\mathrm{e}\mu$ BDT score for events satisfying 70 $< m_{\mathrm{e}\mu} <$ 110 GeV, for simulated signal (red histogram) and background (blue histogram) events. The right-hand plot shows the distribution in $m_{\mathrm{e}\mu}$ of events in the $\mathrm{t} \overline{\mathrm{t}}$ data control sample, for several different BDT thresholds. The vertical error bars in the right-hand plot show the statistical uncertainties.
png pdf	Figure 2-a: The left-band plot shows the unity-normalized distributions of the $\mathrm{Z}\to\mathrm{e}\mu$ BDT score for events satisfying 70 $< m_{\mathrm{e}\mu} <$ 110 GeV, for simulated signal (red histogram) and background (blue histogram) events. The right-hand plot shows the distribution in $m_{\mathrm{e}\mu}$ of events in the $\mathrm{t} \overline{\mathrm{t}}$ data control sample, for several different BDT thresholds. The vertical error bars in the right-hand plot show the statistical uncertainties.
png pdf	Figure 2-b: The left-band plot shows the unity-normalized distributions of the $\mathrm{Z}\to\mathrm{e}\mu$ BDT score for events satisfying 70 $< m_{\mathrm{e}\mu} <$ 110 GeV, for simulated signal (red histogram) and background (blue histogram) events. The right-hand plot shows the distribution in $m_{\mathrm{e}\mu}$ of events in the $\mathrm{t} \overline{\mathrm{t}}$ data control sample, for several different BDT thresholds. The vertical error bars in the right-hand plot show the statistical uncertainties.
png pdf	Figure 3: Fits of the data sidebands with the considered background functions for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In the upper panel of each plot, the black (blue) points with error bars show the data in the sideband (signal) region, while the gray band shows the spread of background estimates from the separate families of parametric functions, the solid red line shows the average prediction, and the dashed green curve shows the $\mathrm{Z}\to\mu\mu^*\to\mu\mu\gamma$ background component. The lower panel shows the ratio of the difference between the data and the average model prediction to the uncertainty of the data with the envelope spread shown in gray.
png pdf	Figure 3-a: Fits of the data sidebands with the considered background functions for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In the upper panel of each plot, the black (blue) points with error bars show the data in the sideband (signal) region, while the gray band shows the spread of background estimates from the separate families of parametric functions, the solid red line shows the average prediction, and the dashed green curve shows the $\mathrm{Z}\to\mu\mu^*\to\mu\mu\gamma$ background component. The lower panel shows the ratio of the difference between the data and the average model prediction to the uncertainty of the data with the envelope spread shown in gray.
png pdf	Figure 3-b: Fits of the data sidebands with the considered background functions for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In the upper panel of each plot, the black (blue) points with error bars show the data in the sideband (signal) region, while the gray band shows the spread of background estimates from the separate families of parametric functions, the solid red line shows the average prediction, and the dashed green curve shows the $\mathrm{Z}\to\mu\mu^*\to\mu\mu\gamma$ background component. The lower panel shows the ratio of the difference between the data and the average model prediction to the uncertainty of the data with the envelope spread shown in gray.
png pdf	Figure 3-c: Fits of the data sidebands with the considered background functions for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In the upper panel of each plot, the black (blue) points with error bars show the data in the sideband (signal) region, while the gray band shows the spread of background estimates from the separate families of parametric functions, the solid red line shows the average prediction, and the dashed green curve shows the $\mathrm{Z}\to\mu\mu^*\to\mu\mu\gamma$ background component. The lower panel shows the ratio of the difference between the data and the average model prediction to the uncertainty of the data with the envelope spread shown in gray.
png pdf	Figure 4: Invariant mass of the $\mathrm{e}\mu$ system for data (points with error bars) and simulated background (stacked filled histograms) events passing the baseline selection without and upper limit on the invariant mass. The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 5: The $\mu\tau_\mathrm{h}$ (left) and $\mu\tau_{\mathrm{e}}$ (right) $m^{{\text{col}}}$ distributions, for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 5-a: The $\mu\tau_\mathrm{h}$ (left) and $\mu\tau_{\mathrm{e}}$ (right) $m^{{\text{col}}}$ distributions, for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 5-b: The $\mu\tau_\mathrm{h}$ (left) and $\mu\tau_{\mathrm{e}}$ (right) $m^{{\text{col}}}$ distributions, for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 6: Distributions of $\mu\tau_\mathrm{h}$ signal and estimated backgrounds in $\alpha_{\mu}$ (left), $\alpha_{\tau}$ (right), for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 6-a: Distributions of $\mu\tau_\mathrm{h}$ signal and estimated backgrounds in $\alpha_{\mu}$ (left), $\alpha_{\tau}$ (right), for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 6-b: Distributions of $\mu\tau_\mathrm{h}$ signal and estimated backgrounds in $\alpha_{\mu}$ (left), $\alpha_{\tau}$ (right), for the data (black markers with error bars), the simulated backgrounds (filled stacked histograms), and a simulated signal with branching fraction $\mathcal{B}(\mathrm{Z}\to\mu\tau) = 10^{-3}$ (blue hatched histogram). The lower panel shows the ratio of the data to simulated yields, with the statistical (combined systematic and statistical) uncertainty of the simulated yield indicated by the filled (striped) gray band.
png pdf	Figure 7: For the $\mathrm{Z}\to\mathrm{e}\mu$ search, the invariant mass fit results for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red) and its separate signal (blue dotted) $\mathrm{Z}\to\mu\mu$ (yellow dash-dotted) and continuum background (gray dashed) components, and the lower panel shows the deviations of the data from the fit function divided by the data uncertainty.
png pdf	Figure 7-a: For the $\mathrm{Z}\to\mathrm{e}\mu$ search, the invariant mass fit results for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red) and its separate signal (blue dotted) $\mathrm{Z}\to\mu\mu$ (yellow dash-dotted) and continuum background (gray dashed) components, and the lower panel shows the deviations of the data from the fit function divided by the data uncertainty.
png pdf	Figure 7-b: For the $\mathrm{Z}\to\mathrm{e}\mu$ search, the invariant mass fit results for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red) and its separate signal (blue dotted) $\mathrm{Z}\to\mu\mu$ (yellow dash-dotted) and continuum background (gray dashed) components, and the lower panel shows the deviations of the data from the fit function divided by the data uncertainty.
png pdf	Figure 7-c: For the $\mathrm{Z}\to\mathrm{e}\mu$ search, the invariant mass fit results for the BDT score ranges 0.3--0.7 (upper left), 0.7--0.9 (upper right), and 0.9--1.0 (lower). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red) and its separate signal (blue dotted) $\mathrm{Z}\to\mu\mu$ (yellow dash-dotted) and continuum background (gray dashed) components, and the lower panel shows the deviations of the data from the fit function divided by the data uncertainty.
png pdf	Figure 8: Upper limits at 95% CL on the branching fraction $\mathcal{B}(\mathrm{Z}\to\mathrm{e}\mu)$ , for each BDT score range and for the final combined fit. The observed limits are denoted by the markers, while the expected limits with their 68% and 95% uncertainties are denoted by the horizontal dashed lines and green and yellow bands, respectively.
png pdf	Figure 9: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 9-a: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 9-b: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 9-c: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 9-d: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 10: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_{\mu}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 10-a: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_{\mu}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 10-b: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_{\mu}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 10-c: Transformed BDT score fit results for the $\mathrm{Z}\to\mathrm{e}\tau_{\mu}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 11: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 11-a: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 11-b: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 11-c: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 11-d: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_\mathrm{h}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 60, `` $\tau\tau$ ''; (upper right) 60 $< m_{\ell\tau} <$ 85, ``signal-like''; (lower left) 85 $< m_{\ell\tau} <$ 100, `` $\mathrm{Z}\to\ell\ell$ ''; (lower right) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 12: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_{\mathrm{e}}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 12-a: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_{\mathrm{e}}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 12-b: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_{\mathrm{e}}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 12-c: Transformed BDT score fit results for the $\mathrm{Z}\to\mu\tau_{\mathrm{e}}$ channels: (upper left) 40 $< m_{\ell\tau} <$ 50, `` $\tau\tau$ ''; (upper right) 50 $< m_{\ell\tau} <$ 100, ``signal-like''; (lower) 100 $< m_{\ell\tau} <$ 170, ``misID''. In each plot, the top panel shows the fit distributions and the data, the middle panel shows the ratio of the data to the background component (points error bars) as well as the (signal+background) / background component distributions (blue dotted histogram), and the bottom panel shows the pull by bin (light blue) using the total signal+background fit results. Shaded bands show the systematic uncertainties of the background estimate.
png pdf	Figure 13: Observed and expected 95% CL upper limit by category, as well as for the final combined fit, for the $\mathrm{Z}\to\mathrm{e}\tau$ (left) and $\mathrm{Z}\to\mu\tau$ (right) searches. The observed limits are denoted by the markers, while the expected limits with their 68% and 95% uncertainties are denoted by the horizontal dashed lines and green and yellow bands, respectively.
png pdf	Figure 13-a: Observed and expected 95% CL upper limit by category, as well as for the final combined fit, for the $\mathrm{Z}\to\mathrm{e}\tau$ (left) and $\mathrm{Z}\to\mu\tau$ (right) searches. The observed limits are denoted by the markers, while the expected limits with their 68% and 95% uncertainties are denoted by the horizontal dashed lines and green and yellow bands, respectively.
png pdf	Figure 13-b: Observed and expected 95% CL upper limit by category, as well as for the final combined fit, for the $\mathrm{Z}\to\mathrm{e}\tau$ (left) and $\mathrm{Z}\to\mu\tau$ (right) searches. The observed limits are denoted by the markers, while the expected limits with their 68% and 95% uncertainties are denoted by the horizontal dashed lines and green and yellow bands, respectively.
png pdf	Figure 14: Distributions in $m_{\mathrm{e}\mu}$ for the scan points 111 GeV (upper row) and 496 GeV (lower row) from the $\mathrm{Z}^{'}$ search. In each row the BDT score range for the left (right) plot is 0.3--0.7 (0.7--1.0). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red solid) and its separate signal (blue dotted) and background (red dotted) components, the middle panel shows the background subtracted data with the fit signal distribution, and the lower panel shows the deviations of the data from the fit function divided by the fit uncertainty.
png pdf	Figure 14-a: Distributions in $m_{\mathrm{e}\mu}$ for the scan points 111 GeV (upper row) and 496 GeV (lower row) from the $\mathrm{Z}^{'}$ search. In each row the BDT score range for the left (right) plot is 0.3--0.7 (0.7--1.0). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red solid) and its separate signal (blue dotted) and background (red dotted) components, the middle panel shows the background subtracted data with the fit signal distribution, and the lower panel shows the deviations of the data from the fit function divided by the fit uncertainty.
png pdf	Figure 14-b: Distributions in $m_{\mathrm{e}\mu}$ for the scan points 111 GeV (upper row) and 496 GeV (lower row) from the $\mathrm{Z}^{'}$ search. In each row the BDT score range for the left (right) plot is 0.3--0.7 (0.7--1.0). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red solid) and its separate signal (blue dotted) and background (red dotted) components, the middle panel shows the background subtracted data with the fit signal distribution, and the lower panel shows the deviations of the data from the fit function divided by the fit uncertainty.
png pdf	Figure 14-c: Distributions in $m_{\mathrm{e}\mu}$ for the scan points 111 GeV (upper row) and 496 GeV (lower row) from the $\mathrm{Z}^{'}$ search. In each row the BDT score range for the left (right) plot is 0.3--0.7 (0.7--1.0). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red solid) and its separate signal (blue dotted) and background (red dotted) components, the middle panel shows the background subtracted data with the fit signal distribution, and the lower panel shows the deviations of the data from the fit function divided by the fit uncertainty.
png pdf	Figure 14-d: Distributions in $m_{\mathrm{e}\mu}$ for the scan points 111 GeV (upper row) and 496 GeV (lower row) from the $\mathrm{Z}^{'}$ search. In each row the BDT score range for the left (right) plot is 0.3--0.7 (0.7--1.0). In each plot, the upper panel shows the data (points with error bars) together with the fit distribution curve (red solid) and its separate signal (blue dotted) and background (red dotted) components, the middle panel shows the background subtracted data with the fit signal distribution, and the lower panel shows the deviations of the data from the fit function divided by the fit uncertainty.
png pdf	Figure 15: Expected and observed 95% CL upper limits on $\sigma(\mathrm{Z}^{'})\mathcal{B}(\mathrm{Z}^{'}\to\mathrm{e}\mu)$ for $\mathrm{Z}^{'}$ masses between 110 and 500 GeV. The solid black line connects filled circles representing the observed upper limits at the scan points, while the dashed line with filled error bands shows the expected limit.

Tables
png pdf	Table 1: Mass regions for the $\mathrm{Z}\to\mu\tau$ and $\mathrm{Z}\to\mathrm{e}\tau$ fits.
png pdf	Table 2: Sources of systematic uncertainty and their relative impacts on the measured branching fraction, in percent. An entry for a channel to which a source of uncertainty is not applicable is denoted with $\text{---}$ .
png pdf	Table 3: The measured branching fraction with its significance (signif.) and the observed and expected 95% CL upper limits, for each of the $\mathrm{Z}\to\mathrm{e}\mu$ , $\mathrm{Z}\to\mathrm{e}\tau$ , and $\mathrm{Z}\to\mu\tau$ decay channels. The prior best published limits are also given for comparison. Included are results for the separate BDT bins for $\mathrm{Z}\to\mathrm{e}\mu$ and the separate $\tau$ decay subchannels for $\mathrm{Z}\to\mathrm{e}\tau$ and $\mathrm{Z}\to\mu\tau$ .

Summary

A search is presented for charged lepton flavor-violating decays of the Z boson, and for the presence of a heavier vector boson

$\mathrm{Z}^{'}$ exhibiting such decays. The data from proton-proton collisions at 13 TeV were collected with the CMS detector at the LHC, and correspond to an integrated luminosity of 138 fb

$^{-1}$ . The specific decay modes considered are

$\mathrm{Z}^{(\prime)}\to\mathrm{e}\mu$ ,

$\mathrm{Z}\to\mathrm{e}\tau$ , and

$\mathrm{Z}\to\mu\tau$ . No significant excess of events over backgrounds from standard-model processes is observed. Upper limits of 1.9

$\times10^{-7}$ , 13.8

$\times10^{-7}$ , and 12.0

$\times10^{-7}$ at 95% CL are set on the branching fractions for

$\mathrm{Z}\to\mathrm{e}\mu$ ,

$\mathrm{Z}\to\mathrm{e}\tau$ , and

$\mathrm{Z}\to\mu\tau$ , respectively. The limit for

$\mathrm{Z}\to\mathrm{e}\mu$ is the most restrictive to date, while for

$\mathrm{Z}\to\mu\tau$ the sensitivity in terms of the expected limit is the same as that of the previous best limit. For

$\mathrm{Z}^{'}$ masses in the range 110--500 GeV, upper limits on the cross section times the branching fraction to

$\mathrm{e}\mu$ range from 0.3 to 7\unitfb, and are the most restrictive to date for this mass range.

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